Determine which of the graphs is the graph of a system of inequalities with no solutions.(1 point)

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A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.
Image with alt text: A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.

A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A solid line with arrows at both ends is plotted, and various regions of the graph are marked.
Image with alt text: A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A solid line with arrows at both ends is plotted, and various regions of the graph are marked.

Two dashed lines and four points are graphed on a coordinate plane. The x-axis ranges from negative 6 to 30 in increments of 2. The y-axis ranges from negative 5 to 15 in increments of 1.
Image with alt text: Two dashed lines and four points are graphed on a coordinate plane. The x-axis ranges from negative 6 to 30 in increments of 2. The y-axis ranges from negative 5 to 15 in increments of 1.

A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.
Image with alt text: A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.
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Answer 1

In the context of systems of inequalities, a system has no solutions when the shaded regions defined by the inequalities do not overlap or intersect at all, meaning there is no point that satisfies all inequalities simultaneously.

From the descriptions you provided:

1. Graph with 2 solid lines - This potentially forms two regions that might intersect or may not, depending on their placement.

2. Graph with 1 solid line - This may represent a situation with potential solutions unless it bounds a specific area where no points can exist.

3. Graph with 2 dashed lines and four points - Dashed lines indicate inequalities, so there may be overlapping regions. However, without seeing the graph, I can't determine if they do intersect or create a solution space.

4. Graph with 2 solid lines again - Similar to the first graph, the lines could either intersect or form a bounded region depending on their orientation.

To determine which graphs have no solutions, we mainly look for configurations where lines create completely separate regions, meaning one inequality completely excludes the area defined by another.

If the lines are both solid and run parallel with one completely above/below the shaded region of the other, then that suggests no solutions.

If you can provide specific placements of the lines or the regions they define for any of the graphs, I can help more accurately identify which set of inequalities might produce no solutions.